There's no such feature in the core, but I suppose you know that since this is in the add-on requests forum.
I'm not aware of any XF1 or XF2 add-on to do this, either.
You are able to export them with an SQL query and backup the data of the messages deleted, but this won't get it in pdf format (not sure why you'd want it as pdfs, it would make it very difficult to index and search the results).